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We demonstrated that an initial phase mismatch in type I second-harmonic generation processes with ultrahigh intensity laser pulses can be used to compensate for third-order nonlinearity not only in temporal profiles but also in spatial distributions of fundamental and second-harmonic pulses. The spatial profile of the second-harmonic pulse shows a good reappearance of the input fundamental pulse throughout the compensation for the third-order nonlinearity.We demonstrated that a frequency chirp initially introduced to fundamental pulse can be used to effectively suppress cubic nonlinear effect in a type I second-harmonic generation with ultra-high intensity laser pulses. The energy conversion efficiency can be increased by a factor of 1.23 with good temporal and spatial profiles of second-harmonic pulse in comparison with conventional schemes of second-harmonic generation.Theoretical analysis and numerical calculation for cascading effects in type I second-harmonic generation are described for two cases as the following: (1) a type I second-harmonic generation provided that group-velocity mismatch, group-velocity dispersion, diffraction, walk-off and absorption can be neglected; (2) a type I second-harmonic generation with picosecond laser pulses involved the group-velocity mismatch, group-velocity dispersion and walk-off. In addition, numerical results for a type I second-harmonic generation with a KDP crystal are also given.We propose a simple OPCPA scheme to increase the energy conversion efficiency from the pump to seed by introducing a time delay between the long pump and short seed pulses so that the seed pulse interacts with all portions of the pump pulse, and the gain is guaranteed simultaneously. We will present numerical results for the proposed OPCPA scheme and demonstrate that the pump energy can be efficiently transferred into the seed and idler pulses.